reset

A Boolean that specifies whether to reset the internal state of the node.

True

Resets the internal state of the node.

False

Does not reset the internal state of the node.

This input is available only if you wire a complex double-precision, floating-point number to FFT{x}.

Default: False

FFT{x}

Complex valued input sequence, which should be conjugated centrosymmetric except for the first element.

This node uses only the anterior half of FFT{x}.

This input accepts the following data types:

Complex double-precision, floating-point number

1D array of complex double-precision, floating-point numbers

2D array of complex double-precision, floating-point numbers

sample length

Length of each set of data. The node performs computation for each set of data.

sample length must be greater than zero.

This input is available only if you wire a complex double-precision, floating-point number to FFT{x}.

Default: 100

shift?

A Boolean that determines whether the DC component is at the center of the FFT of the input sequence.

True

The DC component is at the center of the FFT{x}.

False

The DC component is not at the center of the FFT{x}.

This input is available only if you wire a 1D array of complex double-precision, floating-point numbers or a 2D array of complex double-precision, floating-point numbers to FFT{x}.

How This Input Affects 1D FFT

The following table illustrates the pattern of the elements of FFT{x} with various length of the FFT, when shift? is False. Y is FFT{x} and n is the length of the FFT:

n is even (k = n/2)

n is odd (k = (n-1)/2)

Array Element

Corresponding Frequency

Array Element

Corresponding Frequency

Y0

DC component

Y0

DC component

Y1

Δ
f

Y1

Δ
f

Y2

2
Δ
f

Y2

2
Δ
f

Y3

3
Δ
f

Y3

3
Δ
f

⋅
⋅
⋅

⋅
⋅
⋅

⋅
⋅
⋅

⋅
⋅
⋅

Yk-2

(
k
−
2
)
Δ
f

Yk-2

(
k
−
2
)
Δ
f

Yk-1

(
k
−
1
)
Δ
f

Yk-1

(
k
−
1
)
Δ
f

Yk

Nyquist Frequency

Yk

k
Δ
f

Yk+1

−
(
k
−
1
)
Δ
f

Yk+1

−
k
Δ
f

Yk+2

−
(
k
−
2
)
Δ
f

Yk+2

−
(
k
−
1
)
Δ
f

⋅
⋅
⋅

⋅
⋅
⋅

⋅
⋅
⋅

⋅
⋅
⋅

Yn-3

−
3
Δ
f

Yn-3

−
3
Δ
f

Yn-2

−
2
Δ
f

Yn-2

−
2
Δ
f

Yn-1

−
Δ
f

Yn-1

−
Δ
f

The following table illustrates the pattern of the elements of FFT{x} with various length of the FFT, when shift? is True. Y is FFT{x} and n is the length of the FFT:

n is even (k = n/2)

n is odd (k = (n-1)/2)

Array Element

Corresponding Frequency

Array Element

Corresponding Frequency

Y0

-(Nyquist Frequency)

Y0

−
k
Δ
f

Y1

−
(
k
−
1
)
Δ
f

Y1

−
(
k
−
1
)
Δ
f

Y2

−
(
k
−
2
)
Δ
f

Y2

−
(
k
−
2
)
Δ
f

Y3

−
(
k
−
3
)
Δ
f

Y3

−
(
k
−
3
)
Δ
f

⋅
⋅
⋅

⋅
⋅
⋅

⋅
⋅
⋅

⋅
⋅
⋅

Yk-2

−
2
Δ
f

Yk-2

−
2
Δ
f

Yk-1

−
Δ
f

Yk-1

−
Δ
f

Yk

DC component

Yk

DC component

Yk+1

Δ
f

Yk+1

Δ
f

Yk+2

2
Δ
f

Yk+2

2
Δ
f

⋅
⋅
⋅

⋅
⋅
⋅

⋅
⋅
⋅

⋅
⋅
⋅

Yn-3

(
k
−
3
)
Δ
f

Yn-3

(
k
−
2
)
Δ
f

Yn-2

(
k
−
2
)
Δ
f

Yn-2

(
k
−
1
)
Δ
f

Yn-1

(
k
−
1
)
Δ
f

Yn-1

k
Δ
f

How This Input Affects 2D FFT

The illustration below shows the effect of shift? on the 2D FFT result:

2D input signals

FFT without shift

FFT with shift

Default: False

error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error

error in contains an error

If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

x

Inverse real FFT of the complex valued input sequence.

This output can return a 1D array of double-precision, floating-point numbers or a 2D array of double-precision, floating-point numbers.

error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error

error in contains an error

If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Conjugated Centrosymmetric Property of 1D Inverse Real FFT

When shift? is False and FFT{x} is the Fourier transform of a 1D real time-domain signal with length N, the posterior half part of FFT{x} can be constructed by the anterior half part. The centrosymmetric relationship between the anterior and posterior half part of FFT{x} can be written as

Conjugated Centrosymmetric Property of 2D Inverse Real FFT

When shift? is False and FFT{x} is the Fourier transform of a 2D real time-domain signal with M rows and N columns, the lower half part of FFT{x} can be constructed by the upper half part. The centrosymmetric relationship between the upper and lower half part of FFT{x} can be written as